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DEVELOPMENT OF INTEGRATED MICROWAVE , iS a COMPONENTS FOR GROUND-BASED PHASED ARRAYS
(ELECTRONIC STEERING MODULE)
January 1968
Lincoln Laboratories Project No. C-595, dated 17 April 1967 USAF Contract AF 19 (628)-5167
0
By
Jim Austin Lafe R. Pfieffer, Jr.
Prepared for Lincoln Laboratories
Massachusetts Institute of Technology P. O. Box 73, Lexington, Massachusetts 02173
Texas Instruments Incorporated P. O. Box 5012
Dallas, Texas 75222
flMXurf^a
v proved for public release and M1« This document has been approved for P
its distribution is ununuted.
Final Technical Documentary Report
DEVELOPMENT OF INTEGRATED MICROWAVE COMPONENTS FOR GROUND-BASED PHASED ARRAYS
(ELECTRONIC STEERING MODULE)
January 1968
Lincoln Laboratories Project No. C-595, dated 17 April 1967 USAF Contract AF 19 (628)-5167
By
Jim Austin Lafe R. Pfieffer, Jr.
Prepared for Lincoln Laboratories
Massachusetts Institute of Technology P. O. Box 73, Lexington, Massachusetts 02173
Texas Instruments Incorporated P. O. Box 5012
Dallas, Texas 75222
Report No. 03-68-03
ABSTRACT
This is the final technical documentary report
for the Electronic Steering Module program, Contract
No. C-595, prepared for Lincoln Laboratories, Mass-
achusetts Institute of Technology. This report doc-
uments all efforts expended from contractural start
date, 17 April 1967, to 15 January 1968. The over-
all goal of this program was to design an element
steering module that would be easily produced in
large quantities at a minimum cost. The effort of
this program was directed toward the design of the
ESM module in a microstrip form utilizing thin-film
techniques to form the resistors, capacitors and
transmission-time elements on a ceramic substrate.
Barnes E. Austin Tom M. Hyltm Program Manager Manager, Advanced Development
Microwave Products Department / •1
<< /Y. I M—. -* VirgilJL. Simmons Manager, Microwave Products Department
Accepted for the Air Foroe Franklin C. Hudson Chief .Lincoln Laboratory Of f loo
in
Report No. 03-68-03
FOREWORD
Program Director: Mr. Carl Blake Lincoln Laboratory Massachusetts Institute of Technology
P. O. NO. C-595, dated 17 April 1967
Report Period: 17 April 1967, to 15 January 1968
Submitted: January 196 8
Acknowledgement of Sponsorship: USAF Contract AF19(628)-5167
Priority Rating DX-A7
Report No. 0 3-68-0 3
TABLE OF CONTENTS
SECTION
I.
II.
III.
IV.
TITLE PAGE
INTRODUCTION 1
DESCRIPTION OF SYSTEM 3
CIRCUIT DEVELOPMENT 5
A. Phase Shifter 5
B. Up-Convertor 9
CONCLUSION 17
APPENDIX I CLOSED-FORM SOLUTION FOR THE DESIGN PARAMETERS OF A SINGLE-SECTION LOADED-LINE-TYPE PHASE SHIFTER
APPENDIX II ANALYSIS OF THE STEP ELASTANCE DIODE FOR USE IN AN UP-CONVERTOR
LIST OF ILLUSTRATIONS
FIGURE
1.
2.
3.
4.
5.
b.
TITLE
Block Diagram and Parameters for Element Steering Module (ESM)
Schematic Diagram, 4-Bit Phase-Shift Network
90° Phase-Shift Section
180° Phase-Shift Section
Up-Convertor Schematic
Up-Convertor Mask
PAGE
4
6
7
8
11
15
VI1
Report No. 03-68-03
Texas Instruments Incorporated Components Group
Microwave Products Department
January 196 8
Final Report Electronic Steering Module
Reference: Massachusetts Institute of Technology, Lincoln Laboratory, P.O. Box 73, Lexington, Massachusetts 02173, Purchase Order No. C595 dated 4/17/67.
Acknowledgement: USAF Contract AF19(628)-5167
SECTION I
INTRODUCTION
This is the final technical documentary report for the Ele-
ment Steering Module program, Contract No. C-595, prepared for
Lincoln Laboratories, Massachusetts Institute of Technology.
This report documents effort expended from contractual start
date, 17 April 1967, to 15 January 1968.
The overall goal for the element steering module development
program was to produce a module design that was easily produced
in large quantities at a minimum cost. The large quantity, low-
cost goal is necessary for the use of this type module in large
phased-array defense-type radars. The effort of this program was
directed toward the design of the ESM module in a microstrip form
utilizing thin-film techniques to form the resistors, capacitors
and transmission line elements on a ceramic substrate. The mix-
ing and switching diodes in a beam-lead form are attached to the
thin-film circuit by thermal-compression bonding or another simi-
lar process.
Report No. 03-68-03
This hybrid approach is the most economical form for micro-
wave circuits, such as the ESM module, involving filter structures
in the 1 to 10-GHz range that require a large area for implementa-
tion. The thin-film approach, using photo-etching techniques, is
also capable of high-reproducibility which allows the circuits to
be mass produced without the necessity for tuning adjustments.
Report No. 03-68-03
SECTION II
DESCRIPTION OF SYSTEM
A block diagram and parameters for the proposed element steer-
ing module are shown in Figure 1. It is divided into two basic,
functional sections, a phase shifter and a frequency translator (or
up-convertor). The purpose of the ESM module is to provide beam
steering and frequency translation for a large, phased-array re-
ceiving system. The beam steering is accomplished by adjusting
the phase of a 4.725 MHz pump signal for a variable reactance up-
convertor. The input to the up-convertor is a 500 MHz band from
0.7 to 1.2 MHz converted to the upper side-band from 5.425 to
5.925 MHz.
The phase is shifted in 22.5° increments using a 4-bit binary
scheme. This is accomplished by using diodes to switch the values
of a shunt reactance across a transmission line to produce incre-
mental phase shifts of 22.5°, 45°, 90°, and 180°. The advantages
of this type phase shifter are: small in size, light in weight
and, it is easily controlled by standard low-level integrated-
logic circuits.
The up-convertor was proposed rather than a conventional mixer
due to a 3-dB gain that can be realized rather than the approxi-
mately 8-dB loss resulting in the use of a mixer. The up-convertor
system results in a net 11-dB system gain. This up-convertor cir-
cuit consists of a low-pass filter at the input, a band-pass filter
at the output, and a varactor diode with the pump-tuning circuitry
connected in series between the input and output filters. The
varactor diode is the step-elastance type and was chosen rather
than the usual variable-capacitance type in order to reduce the
conversion-gain variations occuring with pump-power variations
using a variable-capacitance diode.
Report No. 03-68-03
PHASE SHIFTER
PUMP
• IN
FOUR BIT
360° PHASE
SHIFTER
IFI
IN
0.7-1.2 GHz BAND PASS
FILTER
4.725 GHz
BAND PASS FILTER
5.425-5.925 GHz BAND PASS
FILTER
IF2 —O OUT
rtt UP-CONVERTER
ELEMENT STEERING MODULE SPECIFICATIONS
INPUT FREQUENCY 700 - 1200 MHz
OUTPUT FREQUENCY 5.425 - 5.925 GHz PUMP FREQUENCY 4.725 GHz
PUMP PHASE SHIFTER 4 BITS
PHASE TRACKING ACCURACY A*max - 6°rms FROM AVG.
PHASE SHIFTER SWITCHING TIME 3 \>S>
PUMP POWER 5omw LOWER SIDEBAND ISOLATION 20 dB PUMP ISOLATION 20 <!B
CONVERSION GAIN >0dB AMPLITUDE TRACKING + 1 (IB INPUT/OUTPUT IMPEDANCE 50 U INPUT/OUTPUT VSWR 1 .5 INPUT LEVEL FOR 1 (IB OF COMPRESSION 0 dBm
SC06941
Figure 1. Block Diagram and Parameters for Element Steering Module (ESM)
Report No. 03-6 8-03
SECTION III
CIRCUIT DEVELOPMENT
A. PHASE SHIFTER
The schematic diagram of the proposed phase-shift network is
shown in Figure 2. This is a diode-loaded line-type phase-shift
network and has been discussed by J. F. White.— This is an
iterative-type circuit, having a canonical form consisting of a
length of transmission line symmetrically loaded at its ends by
small susceptances whose values are switched by means of diodes.
The value of the susceptances, the line impedance, and the line
length are chosen to obtain the desired phase shift while, at the
same time, maintaining a low VSWR by mutually cancelling the re-
flections produced by the susceptances. This type of phase
shifter is capable of handling high power by designing each sec-
tion for small phase shifts (<22.5°) which in effect decouples
the diode from the main transmission line. It can be shown that
this also allows operation over a wider bandwidth for a given
phase error.
The disadvantage of designing for a low phase shift per sec-
tion is the larger number of sections required for a given total
phase shift. The proposed phase-shift network shown in Figure 2
uses a 22,5°-section and seven 45°-sections to obtain a 4-bit (or
16-step) 360°-phase shift. The 90° and 180°-bits were realized
by combining the appropriate number of 45°-sections. In order
to reduce the number of sections, and hence the size and cost, a
study was made of realizing 90° and 180°-bits with other than 45°-
sections. The only logical possibility is a 90°-section, using
one for the 90°-bit and two for the 180°-bit.
Report No. 03-68-03
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Report No. 03-6 8-03
A general closed-form solution for the insertion phase of a
single phase-shift section is derived in Appendix I. Using the
results from Appendix I the loading susceptances and line impe-
dance are found to be +J20.0 millimhos and 35.3 ohms respectively
The +J20.0 millimho susceptances can be realized by using a diode
with -j 100-ohms reactance when reverse biased in series with a
+j 50-ohm reactance. Turning the diode off and on results in
+j 20.0-millimhos susceptance. A computer run was made for a
single 90°-section and two 90°-sections in cascade. The results
are shown in Figures 3 and 4, respectively. The losses are about
90' Zn • 35 ft
3ft
x = /T» 100 ft
50 ft
CA14 62 6
COMPUTED PERFORMANCE
NORMALIZED
FREQUENCY
DIODE
STATE VSWR
LOSS
dB
INSERTION
PHASE
PHASE
ERROR
0.9 ON 1.60 0.95 - 2 6.7 +50
0.9 OFF 1.66 0.53 -1 1 1.7
1.0 ON 1.08 0.51 - 45.3 +0.5
1 .0 OFF 1.08 0.51 -1 34.8
1 .1 ON 1.48 0.53 - 61.9 -1 8.7
1 .1 OFF 2.64 2.30 -1 70.6
PHASE ERROR = 90° - (0QN - 0OFF)
Figure 3. 90° Phase-Shift Section
Report No. 03-6 8-03
r Q-
6-
.Al 4 02 7
90
ZQ - 35U
90c H 3 £2
X = -^r i oo 11
-6 ;o tt
COMPUTED PERFORMANCE
NORM-
ALIZED
FREQ .
DIODE
STATE VSWR
LOSS
ilB
INSERTION
PHASE
PHASE
ERROR
0.9 ON 2.1 6 2.33 - 52.2 + 6.5
0.9 OFF 1 46 0.62 -225.7
1 0 ON 1 .1 1 1 .0 2 - 90. b + i.:
1 0 OFF 1.11 1.0 2 -269 4
1 1 ON 1 .44 0.82 -1 22 4 -37.3
1 1 OFF 4.9 G.2 0 -339.7
PHASE ERROR 180 - ( <£ON - <£OFF)
Figure 4. 180° Phase-Shift Section
what can be expected using 45°-sections, but the phase shift and
VSWR, with respect to frequency, are worse.
Because manufacturing tolerances will cause a shift in the
center frequency of the produced circuits it was decided to use
45°-sections as originally proposed. However, no circuits had
been produced at the time effort on the program was stopped as a
result of system redirection on Contract AF19(628)-5167.
Report No. 03-68-03
B. UP-CONVERTOR
Frequency translation in the ESM module is performed by an
upper side-band up-convertor. The input frequency band from 0.7
to 1.2 GHz is converted to an upper side band of 5.425 to 5.925
GHz with a pump frequency of 4.725 MHz. The theoretical conver-
sion gain varies from 8.9 dB at 5.425 GHz to 6.94 dB at 5.925 GHz.
In the proposal this was reduced to a 3-dB conversion gain across
the band to account for circuit losses and the necessary fixed
loss at the low end to remove the gain slope. The circuit was
designed using micro-strip lines to realize the filter structures
and thin-film resistors and capacitors for the bias circuit. This
was in accordance with the desire for an all thin-film approach to
meet the cost and reproducibility requirement in large-volume pro-
duction.
The design of wide-band up-convertors has been treated by 2 3/ several authors notably, Getsmger and Matthaei.——' An attempt
was made early in the program to synthesize the input and output
filters following the method of the above authors. In essense,
this consisted of designing the input and output filters as one
composite band-pass filter which was then bisected and coupled
together through the non-linear capacitance of the diode. The
element values of the input and output filters are derived from
the same low-pass prototype and then transformed to band-pass
structures at the appropriate input- and output-frequency bands.
This approach results in an efficient design using the minimum
number of reactive elements.
However, difficulty is encountered in attempting to realize
the above filter design for wide bandwidths using distributed
elements especially y-strip transmission lines. Another problem
was the spurious pass bands of the input band-pass filter that
must be kept away from the lower and upper side bands. These
problems are not insurmountable but were considered beyond the
Report No. 03-68-03
scope of this contract. Because of these difficulties a simpler
approach was taken using a low-pass filter at the input. Although
not as sophisticated as the above technique a working circuit could
be designed and by optimizing element values with the aid of a
computer the design objectives could be achieved.
The circuit consists of a low-pass filter at the input, a
band-pass filter at the output and a varactor diode with the pump
tuning circuitry connected in series between the input and output.
In addition to series tuning the diode at input, output and the
pump frequencies, the composite structure was designed to present
a high-reactive impedance to the diode at the lower side band from
3.525 to 4.025 GHz. This is necessary to prevent any power flow
at the lower side band which would result in undesired gain peaks
in the conversion gain at the upper side band. A schematic dia-
gram of the up-converter is shown in Figure 5. For convenience
in the following discussion the various lines are lettered. Since
the filter and diode tuning circuits are all interacting through
the non-linear properties of the diode they will be discussed in
the order that allows for a minimum iteration in the design ap-
proach .
A step-elastance diode was selected because it offers the
possibility of constant conversion gain and circuit tuning inde-
pendent of pump amplitude. This advantage is based on the fact
that the step-elastance diode is switched between the S and ^ max S states at the pump frequency where S and S are fixed min f t- ^ i max min
diode parameters and are independent of the pump amplitude. The
duty cycle of the two states is a function of the pump amplitude
and will effect circuit performance, but by a suitable choice of
a self-bias resistor, this effect can be minimized. The charac-
teristics of a step-elastance diode in an up convertor are de-
rived in Appendix II. It is shown that a diode with S = +11 d f max
22.9 x 10 , S . equals 0, and a 50% duty cycle pro-
vides a 50-ohm conversion impedance for the input and output
10
Report No. 03-68-03
INPUT LOW-PASS
FILTER
IN O-
PUMP FILTER AND
DIODE TUNING
OUTPUT BAND-PASS
FILTER
r 37
I' r BIAS PUMP
C, • 100 pF, C2 = 0.12 pF, R, =>30K
-QOUT
/h
LINE Zo LENGTH
a soft 0.203
b ss n 0.262
0 soft 0.492
d 33ft 0.128
e soft 0.133
t 50 ft 0.480
g 50 ft 0.405
h 47ft 0.082
i 47 ft 0.492
J Z0 = 37.5
Z0 = 87.5 0.200
CA14628
Figure 5. Up-Convertor Schematic
11
Report No. 03-6 8-03
filters. This is a desirable feature due to the ease of the
design and testing of the filters. A diode with these values
is also readily available in a beam-lead form and will have
virtually zero parasitic elements with which to contend.
The design of the input and output filters is straightforward
because of the 50-ohm impedance level at their respective input
and outputs. The input filter is a maximally flat, 4-element,
low-pass design with a 3-dB cutoff at 1.8 GHz. A small area,
low-pass design was chosen rather than a larger area band-pass
design. Also, spurious pass bands are easier to control in a
low-pass filter than in a band-pass type filter. The low-pass
filter is comprised of lines, a, b, c and d in Figure 5. The
output filter is of the maximally flat, band-pass type v/ith a
3-dB band width of 9 00 MHz which is centered at 5.6 75 GHz. The
band-pass filter is realized using quarter-wave, parallel-
coupled lines (lines j in Figure 5). Its first spurious pass
band is at 17.025 GHz and is outside the frequency band of in-
terest. Both input and output filters were designed without
grounded elements due to the difficulty of obtaining a good RF
ground in a micro-strip medium.
Since a connection to ground is necessary on either side of
the diode for bias purposes it was found convenient to place a
shorted stub (line i Figure 5) at the input of the band-pass
filter. This serves both as a ground return for the diode bias
circuit and, by using a half wave length at the pump frequency,
additional pump filtering at the output is provided. The open
stub (line h Figure 5) provides a capacitive reactance to form
a parallel resonant circuit with the inductive reactance of the
shorted stub at the center of the output frequency band. Later,
the impedance level of lines h and i will be selected to reson-
ate the diode at the input frequency. The remaining dc return is
provided by a thin-film resistor from the input of the low-pass
filter to ground. The shunt impedance of this resistor, at the
12
Report No. 03-6 8-03
input frequencies, is lower than the dc value due to the dis-
tributed capacitance of the thin-film pattern. An approximate
solution for this shunt impedance can be found by solving for
the characteristic impedance of a lossy transmission line. For
a resistor pattern having 50 ohms per square and a 4-mil line
width the impedance was calculated to be 700 -j 700 ohms which
provides a negligible shunt loading at the 50-ohm input impe-
dance of the low-pass filter.
Series tuning for the diode at the input, output, and pump
frequencies is provided by lines e, f, h, and i together with the
impedances at the output of the low-pass filter and the input of
the band-pass filter. It is assumed that the loading effect of
the pump-input filter (line g in Figure 5) is negligible because
of its narrow bandwidth. The impedance level of line f is
selected to be 50 ohms. Since the impedance at the input of the
output band-pass filter (including the parallel-resonant circuit
formed by lines h and i) is also 50 ohms, the length of line f
will not affect the series resonance of the diode at the output
frequency. Since the output impedance of the low-pass filter is
essentially zero at the output frequency, it is only necessary
to adjust the length of line e so that it forms a series-resonant
circuit with the diode capacity at the output frequency. At the
pump frequency the junction of lines h and i is a short circuit
and the output impedance of the low-pass filter is essentially a
short. Therefore, the lingth of line f can be adjusted to series
resonate the diode capacity and line e at the pump frequency.
Finally, the diode is series resonated at the input frequency by
adding a half wave of 50-ohm line (at the pump frequency) to the
length of f and by adjusting the impedance levels of lines h and
i. Neither of these adjustments will affect the tuning of the
diode at the pump and output frequencies.
The pump input filter (line g and capacitors C.) is a narrow-
band, half-wave resonator type with capacitive coupling at the
13
Report No. 03-68-03
ends. The narrow band-width (4%) provides negligible loading on
the circuit at the input and output frequencies. The pump filter
was designed for 50-ohms input and output impedance. It is con-
nected at a point in the diode series resonate circuit where the
diode series resistance (~3 ohms) is transformed to 50 ohms.
This completes the first design of the up-convertor and was
considered sufficient for constructing a development model. A
circuit was constructed using the calculated line lengths and im-
pedances shown in Figure 5. The dc return at the input of the
low-pass filter was provided by a bias tee rather than a thin-
film resistor to expedite the construction. A copy of the photo
mask is shown as Figure 6.
The first circuit constructed was not successful. It was
necessary to lower the pump frequency to approximately 4.5 GHz
before energy could be coupled to the diode circuit. At this
point, by using a panoramic receiver an upper side-band signal
was observed at the output but it was much lower than the pump
signal. The pump input filter was checked separately and found
to be resonant at 4.5 GHz rather than 4.725 GHz. The half-wave
shorted stub was also checked separately and found to be resonant
at 4.675 GHz instead of 4.725 GHz. The error in the pump input
filter was due to fringing capacitance at the ends of the line
which had been neglected in the calculating of the line length.
The error in the half-wave stub length was considered normal for
the first trial circuit. Both lengths were adjusted and a new
mask was ordered. The revised circuit had not been fabricated
at the time system redirection occurred on Contract No. AF19(628)-
5167.
The plans were to obtain test results from the first devel-
opment circuit and do a redesign of the circuit using the com-
puter to optimize the various line lengths.
14
Report No. 03-68-03
M t0 X M <D -P k
> C o u
I
U3
15
Report No. 03-68-03
SECTION IV
CONCLUSION
At the time the system redirection occurred on Contract
AF19(628)-5167 the design study had been completed and the first
model of the steering module up-convertor had been fabricated
and tested. Acceptable test data indicated changes necessary to
meet module operational requirements. The revised circuit had
not been fabricated at the time of redirection. The phase-
shifter study was complete and initial layout was scheduled.
Ancillary circuit functions posed no problem and hardware fabri-
cation was planned.
In conclusion, Texas Instruments feels that the intent of
this program was fulfilled. That is, the basic design approach
was sound, fabrication of the steering module using thin-film
techniques is both feasible and practical, and that the modules
can be mass produced economically and reliably for use in large,
ground-based phased-array radar systems.
17
Report No. 03-68-03
REFERENCES
1. J. F. White, "High Power PIN Diode Controlled, Microwave Trans- mission Phase Shifters", IEEE Transactions on Microwave Theory and Techniques, Vol. MTT- , March 1965, pp. 233-242.
2. G. L. Matthaei, "A Study of the Optimum Design of Wide-Band Parametric Amplifiers and Up-Converters", IRE Transactions on Microwave Theory and Techniques , Vol. MTT- , January 19 61, pp. 23-38.
3. W. J. Getsinger and G. L. Matthaei, "Some Aspects of the De- sign of Wide-Band Up-Converters and Nondegenerate Parametric Amplifiers", IEEE Transactions on Microwave Theory and Tech- niques, Vol. MTT- , January 1964, pp. 77-87.
4. R. P. Rafuse and Paul Penfield, Jr., Varacter Applications, The MIT Press, Massachusetts Institute of Technology, Cam- bridge, Massachusetts, 19 62.
5. L. A. Blackwell and K. L. Kotzebue, Semiconductor-Diode Para- metric Amplifiers, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1961.
6. G. L. Matthaei, Leo Young, and E. M. Jones, Microwave Filters, Impedance-Matching Networks, and Coupling Structures, McGraw- Hill Book Co., New York, N. Y., 1964.
19
APPENDIX I
CLOSED-FORM SOLUTION FOR THE DESIGN PARAMETERS OF A SINGLE-SECTION LOADED-LINE-TYPE PHASE SHIFTER
Report No. 03-68-03
APPENDIX I
CLOSED-FORM SOLUTION FOR THE DESIGN PARAMETERS OF A SINGLE-SECTION LOADED-LINE-TYPE PHASE SHIFTER
The relationship between a loaded-line phase-shifter section
and an equivalent-unloaded uniform transmission line is shown
below.
cos 9 - -KT- sin 0 91 = cos I cos 9 ^— sin 0| (1)
,1/2
'o' -»o[l- X2+2-tCH (2)
For digital phase-shifter applications the values of the loading
susceptances are controlled in a discrete manner by the use of
switching diodes. It is desirous to find a solution for the param-
eters of the loaded-line phase-shifter section given a desired
change in the insertion phase with the contraint that Y =1.
Two special cases of interest are
1) The loading susceptances are switched from +B to -B, and
2) The loading susceptances are switched from zero (0) to some finite value B..
Case 1—Loading susceptances - ± B •
Inserting the constraint Y = 1 into Equation (2) we have
* White, J. F., High Power, PIN Diode Controlled, Microwave Trans- mission Phase Shifters, IEEE - PGMTT, March 1965, pp 233-242.
1-1
Report No. 03-68-03
1 = Y 1 - (v)'"M cot 8 1/2
(3)
Equation (3) is satisfied for +13 and -B only if cot 8 = 0° or
0 = 90°.
Letting 8 = 90° and solving for B in Equation (3) we have
+ 11 - Y and B ="V YQ
(4)
substituting 8 = 90°, B = + ^1 - Y and B ="\ YQ 1 into
Equation (1), we obtain the two following equations
'•'--"(-V'-v') 1 (-v7^)
(5)
8 = cos (6)
Since Y =1 for both +B and -B, the change in insertion phase
is the difference between 6 and 8_ . Let \\> = 8_ be the
desired change in insertion phase. Then
•(.y^r)-~.-'(-V^r)" y = cos
p = cos ' (-V^F)- TT - COS
\\) = 2 cos ' (TFF)- • (9)
1-2
Report No. 03-63-03
I ^ 2 '(V^) | + 1 = cos"1 L 1 - -L0 1 (10)
cos (!+ JW1 " r» (11) » o
-sin I -J1 - 7^2 <12>
,2 i_ _ _L Y.
sin' | - 1 —2 (13)
o
-i-2 - 1 - sin2 f = cos2 f (14)
o
Y = —^_ = sec | (15) cos |
Substituting Y = sec *• into Equation (2) we have
V 2C2 | - 1 (16)
•V 2 i - m.„ 4 B =-•/ Tan *• • Tan £ (17) 2" " xa" 2"
Thus, for the case where the loading susceptances are switched be-
tween +B and -B the parameters are, 6=90°,B=± Tan ty/2 and
T = sec ty/2, where ty is the desired insertion phase.
Case 2—Loading susceptances • 0 and B..
1-3
Report No. 0 3-68-03
1 = Y 1 - «•)''' t cot 1/2
(18)
Equation (18) is satisfied for both B = 0 and B = B, only if
Y = 1. Letting Y = 1 and B = B, in Equation (18), and by squar-
ing both sides, we have
1 « 1 - B. + 2 Q cot 9 (19)
B, = 2 cot e (20)
Substituting Y = 1, B - 0 and B = 2 cot 0 into Equation (1), we
obtain the following two equations
= cos (cos 9) = 8
B. = cos (cos 9 -2 cot 0 sin 9)
(21)
B1 = cos (-cos 9) = IT - 9 (22)
Let ty = 0 B- be the desired change in insertion phase as
in Case 1. Then
^ = G- (TT-6) =28-TI
A - ^ + ff 9 " 2 + 2"
(23)
(24)
Substituting the value for 9 in Equation (24) into Equation (20)
we have
B, =
B, =
2 cot f + \
-2 Tan J
(25)
(26)
1-4
Report No. 03-68-03
Thus, for the case where the loading susceptances are switched
between zero and B.. the parameters are Y = 1, B, = -2 Tan rp/2 and
9 = ty/2 + TT/2 , where ty is the desired change in insertion phase.
1-5
APPENDIX II
ANALYSIS OF THE STEP-ELASTANCE DIODE FOR USE IN UP-CONVERTOR
Report No. 03-68-03
APPENDIX II
ANALYSIS OF THE STEP ELASTANCE DIODE FOR USE IN AN UP-CONVERTOR
The step-elastance diode for the purpose of this analysis is
assumed to have an elastance S = 1/c of zero when the diode is in
the conducting state; and a constant elastance of S when the 3 max diode is turned off. The diode series resistance is assumed neg-
ligible. Beam-lead diodes are available which are very good ap-
proximations of the above. We will also assume that the diode is
pumped so that it changes state each one-half cycle of the pump
frequency producing the following elastance V time curve. The 9
S MAX
n <x)p
27T
Wp
elastance, as pumped, can be written in Fourier series
S ( «- so+ L s*e jkwpt k = -00
II-l
where
Report No. 03-68-03
S, = max kn , when k is odd
S = O, when k is even
S0 = max
If the diode is open-circuited at ,all frequencies except the in-
put, pump and upper sideband frequencies, we can write the small
signal equations as follows
V
V . u_
3W«
Dw,
301 u
JuJ u
I L uj
t The notation follows that of Penfield and Rafuse, where the sub-
scripts s and u refer to the input and upper sideband frequencies
respectively. The optimum source and load resistance for maxi-
mum gain and minimum noise figure has been solved using the above
equations and is as follows
R opt .as » s u
It is convenient in designing the input and output filters to
work at an impedance level of 50 ohms. For an input center fre-
quency of 0.95 GHz and an output center frequency of 5.675 GHz
the value of S = TTS, is calculated to be 22.9 x 10 . This max 1 corresponds to a diode with a reverse bias capacity of 0.536 pF.
The average capacity under pumping conditions will be twice this
tPenfield, P., and Rafuse, R. P., "Varactor Applications," The MIT Press, Cambridge, Mass. (1962).
II-2
Report No. 03-6 8-03
value or 0.872 pF. This average capacitance must be incorporated
in the design of the input, output, and pump filter circuits.
It is interesting to note that the elastance wave form pro-
duced by the pump signal can also be generated by periodically
opening and closing a switch connected across a capacitor. This
is not a valid equivalent circuit for the pumped-step elastance
diode in an up-convertor circuit since the Manley-Rowe power for-
mulas require the power at the pump and signal frequencies inter-
act in the nonlinear reactance. If we applied a signal to such a
switched capacitor we would expect sidebands to be generated, but
there should be no conversion gain.
II-3
UNCLASSIFIED Security Classification
DOCUMENT CONTROL DATA - R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified)
I, ORIGINATING ACTIVITY (Corporate author)
Texas Instruments Incorporated under Purchase Order C-595 to M.I.T. Lincoln Laboratory
2a. REPORT SECURITY CLASSIFICATION Unclassified
2b. GROUP None
3. REPORT TITLE
Development of Integrated Microwave Components for Ground-Based Phased Arrays (Electronic Steering Module)
4. DESCRIPTIVE NOTES (Type of report and inclusive dates)
Final Technical Documentary Report
S. AUTHOR(S) (Last name, first name, initial)
Austin, Jim and Pfieffer, Lafe R., Jr.
6. REPORT DATE
January 1968 7a. TOTAL NO. OF PAGES
44 7b. NO. OF REFS
8a. CONTRACT OR GRANT NO. AF 19(628)-5167
b. PROJECT NO.
ARPA Order 498
9a. ORIGINATOR'S REPORT NUMBER(S)
03-68-03
96. OTHER REPORT NO(S) (Any other numbers that may be assigned this report)
ESD-68-53
10. AVAILABILITY/LIMITATION NOTICES
This document has been approved for public release and sale; its distribution is unlimited.
II. SUPPLEMENTARY NOTES
None
12. SPONSORING MILITARY ACTIVITY
Advanced Research Projects Agency, Department of Defense
13. ABSTRACT
This is the final technical documentary report for the Electronic Steering Module program, Contract No. C-595, prepared for Lincoln Laboratory, Massachusetts Institute of Technology. This report documents all efforts expended from the contractual start date, 17 April 1967, to 15 January 1968. The overall goal of this program was to design an element steering module that would be easily produced in large quantities at a minimum cost. The effort of this program was directed toward the design of the ESM in a microstrip form utilizing thin-film techniques to form the resistors, capacitors and transmission-time elements on a ceramic substrate.
14. KEY WORDS
microwave equipment electronic equipment
phased array radars electronic steering module
UNCLASSIFIED
Security Classification